Many modes of Scanning Probe Microscopy are based on resonant detection. Typically an oscillating cantilever having a sharp tip is excited at one of the resonant frequencies of the cantilever. When the tip is brought close to a surface, atomic forces, magnetic forces (if the tip is magnetic), electrostatic forces (if the tip is charged) or other tip-surface interactions are measured by detecting a change in the amplitude and/or phase of the cantilever oscillation. This amplitude and phase change is measured at the same frequency that the cantilever is excited, typically by lock-in methods. In Atomic Force Microscopy (AFM), this type of resonant detection was originally demonstrated by Binnig, Quate and Gerber [B. Binnig et. al, Phys. Rev. Lett. vol. 56, 930 (1986); Y. Martin et al. J. Appl. Phys. vol. 61, 4723 (1987); T. R. Albrecht et al. J. Appl. Phys. vol. 69, 668 (1991)] but today it is frequently called “tapping mode AFM” [Tapping mode AFM is a Veeco trade mark. U.S. Pat. No. 5,412,980, U.S. Pat. No. 5,519,212 (1996), U.S. Pat. Reissue No. RE36,488 (2000); Q. Zhong et al. Surf. Sci. Lett. vol. 290, L668 (1993)], and many variations on this basic method exist, such as Magnetic Force Microscopy (MFM) and others. The oscillating cantilever can be replaced with other types of mechanical resonators to increase the quality factor and frequency of the resonator. The signal to noise ratio with this method is improved when the quality factor of the resonator is increased, and the sensitivity and measurement bandwidth are improved when the frequency of the resonator is increased. To optimize these qualities simultaneously, one desires a resonator which, when it is freely oscillating away from the surface, maintains a response which is as linear as possible for as large an oscillation amplitude as possible.
The Atomic Force Microscope (AFM) has emerged as a key tool in many nanotechnology applications, providing unprecedented contrast for atomic-scale variations in surface topography. In AFM, a cantilever with a sharp tip at the free end is scanned over a surface, and the deflection of the cantilever is measured, typically with the so-called optical lever. A force between the surface and the tip causes the bending of the cantilever (like a spring) which is read out by the optical lever as deflection of the cantilever. If the spring constant of the cantilever is known, and the deflection system is properly calibrated, the force between the tip and the surface can be determined.
AFM can be run in two basic modes: The first mode is a quasi-static mode (also called Contact Mode AFM), where the inertia (effective mass) of the cantilever is neglected in the description of the cantilever dynamics. The second mode is the so-called dynamic mode (also called Tapping Mode AFM), which takes the inertia of the cantilever into account. Dynamic mode AFM exploits a mechanical resonance (typically the fundamental bending mode) of the cantilever to enhance the force sensitivity. This enhanced sensitivity allows for imaging with lower average back-action force on the sample, thereby causing less damage to soft and delicate samples than is the case with quasi-static AFM. However, Dynamic AFM has been limited in its ability to extract information about the chemical or elastic properties of the sample surface. Such information is contained in the so-called force-distance curve (force as a function of tip-surface distance). Force-distance curves can be measured in quasi-static mode by a slow process with limited sensitivity that is not done simultaneously with scanning [W. F. Heinz and H. H. Hoh, J. Chem Educ., vol. 82, 695 (2005), H. J. Butt, Biophys. J., vol. 63, 578 (1992)].
Thus, there has been great interest in the AFM community in the development of methods for extracting the nonlinear force-distance relationship with Dynamic AFM. Some methods have been developed which are based on analysis of the higher harmonics (or integer multiples) of the frequency of free cantilever oscillation [U.S. Pat. No. 6,935,167 (2005); R. W. Stark and W. M. Heckl, Rev. Sci. Instrum. vol. 74, 5111 (2003); M. Balantekin and A. Atalar, Appl. Phys. Lett. vol. 87, 243513 (2005); S. Crittenden, A. Raman and R. Reifenberger, Phys. Rev. B, vol. 72, 235422 (2005)] (by free cantilever oscillation, we mean oscillation in the absence of the tip-surface force) or harmonics of a torsional cantilever motion [U.S. Pat. No. 7,089,787, U.S. Pat. No. 7,302,833; O. Sahin et. al. Sens. Actuators A, vol. 114, 183 (2004); O. Sahin et al. Nat. Nanotechnology, vol. 2, 507 (2007)]. Because these harmonics do not coincide with bending eigenmodes of standard cantilevers, methods based on harmonics require special cantilevers in order to get appreciable response at the harmonic frequencies. Some of these cantilevers require a more complex readout system, and in any case, large measurement bandwidth is required to capture the harmonic progression. These problems limit the sensitivity of harmonic methods. Other Dynamic AFM methods which claim to extract additional tip-surface force information use two drives frequencies which excite the cantilever at two flexural eigenmodes, measuring response at these two frequencies [J. Lozano and R. Garcia, Phys. Rev. Lett. vol. 100, 076102 (2008); N. F. Martinez et. al, Appl. Phys. Lett. vol. 89, 153115 (2006), R. Proksch, Appl. Phys. Lett., vo. 189, 113121 (2006)]. These so-called Dual-AC techniques also require large measurement bandwidth, and have very limited information content, because they only collect response at two frequencies.
Here we describe a new method of Dynamic AFM which is based on the intermodulation of two or more drive frequencies. The use of Intermodulation in AFM was disclosed in a previous provisional patent application by us [USPTO Provisional pat. No. 60990518 (EFS ID 2515284, confirmation nr. 8137)]. Here we also describe additional methods of driving the cantilever which have advantages over those previously disclosed. We also describe methods of analysis of the spectrum of intermodulation products, which allow one to extract the force-distance curve. We call these methods of analysis Intermodulation Fingerprinting and Intermodulation Force Spectroscopy [USPTO Provisional pat. No. 61/096,370 confirmation nr. 4316].